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Extremes in the complexity of computing metric distances between partitions
1Department of Computer Science, Memorial University of Newfoundland, St. John's, Nfld., Canada A1C 5S7.
IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
Summary
This study introduces an analytical model for minimum-length sequence (MLS) metrics to measure distances between set partitions. It highlights how different MLS metrics, though similar, can have vastly different computational complexities, with one being NP-complete.
Area of Science:
- Computational mathematics
- Data analysis
- Algorithm analysis
Background:
- Minimum-length sequence (MLS) metrics are used to quantify distances between partitions of a set.
- Understanding the computational complexity of these metrics is crucial for practical applications.
Purpose of the Study:
- To present an analytical model for MLS metrics.
- To enable users to select appropriate MLS metrics for their classification tasks.
- To investigate the computational complexities associated with different MLS metrics.
Main Methods:
- Development of an analytical model for MLS metrics.
- Analysis of computational complexities for various MLS metrics within the model.
Main Results:
- The analytical model allows for the identification of suitable MLS metrics based on user-defined criteria.
- While some MLS metrics exhibit linear time complexity, a closely related metric is shown to be NP-complete.
- Significant differences in computational complexity exist even among seemingly similar MLS metrics.
Conclusions:
- The choice of MLS metric can drastically impact computational performance.
- Users must consider both metric appropriateness and computational feasibility for classification applications.
- The NP-completeness of certain MLS metrics necessitates careful algorithm selection for large datasets.
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